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The $t$-covering number $\\tau_t(\\mathcal{F})$ of $\\mathcal{F}$ is defined as the minimum size of a set $T$ such that $|F\\cap T|\\geq t$ for all $F\\in \\mathcal{F}$. For positive integers $k_1$ and $k_2$, let $\\mathcal{F}_i$ be a collection of $k_i$-subsets of $[n]$ for $i\\in \\{1,2\\}$. The families $\\mathcal{F}_1$ and $\\mathcal{F}_2$ are said to be cross $t$-intersecting if $|F_1\\cap F_2|\\geq t$ for all $F_1\\in\\mathcal{F}_1$ and $F_2\\in \\mathcal{F}_2$. 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The $t$-covering number $\\tau_t(\\mathcal{F})$ of $\\mathcal{F}$ is defined as the minimum size of a set $T$ such that $|F\\cap T|\\geq t$ for all $F\\in \\mathcal{F}$. For positive integers $k_1$ and $k_2$, let $\\mathcal{F}_i$ be a collection of $k_i$-subsets of $[n]$ for $i\\in \\{1,2\\}$. The families $\\mathcal{F}_1$ and $\\mathcal{F}_2$ are said to be cross $t$-intersecting if $|F_1\\cap F_2|\\geq t$ for all $F_1\\in\\mathcal{F}_1$ and $F_2\\in \\mathcal{F}_2$. 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